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matlab 数学建模

2008-6-18 13:59:14  5267 MATLAB
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<p><font face="Verdana">matlab 数学建模教程</font><br/></p>
<p>&nbsp; </p>
<p class="MsoNormal" style="TEXT-ALIGN: center" align="center"><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">第一章</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><span style="mso-spacerun: yes">&nbsp; </span></span></b><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">线性规划</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">§</span><span lang="EN-US">1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">线性规划</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">在人们的生产实践中,经常会遇到如何利用现有资源来安排生产,以取得最大经济效益的问题。此类问题构成了运筹学的一个重要分支—数学规划,而线性规划</span><span lang="EN-US">(linear Programming </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">简记</span><span lang="EN-US">LP)</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">则是数学规划的一个重要分支。自从</span><span lang="EN-US">1947</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年</span><span lang="EN-US">G. B. Dantzig </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">提出求解线性规划的单纯形方法以来,线性规划在理论上趋向成熟,在实用中日益广泛与深入。特别是在计算机能处理成千上万个约束条件和决策变量的线性规划问题之后,线性规划的适用领域更为广泛了,已成为现代管理中经常采用的基本方法之一。</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span lang="EN-US">1.1 </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">线性规划的实例与定义</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">例</span><span lang="EN-US">1 <span style="mso-spacerun: yes">&nbsp;</span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">某机床厂生产甲、乙两种机床,每台销售后的利润分别为</span><span lang="EN-US">4000</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">元与</span><span lang="EN-US">3000</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">元。生产甲机床需用</span><span lang="EN-US"><span style="POSITION: relative; TOP: 3pt; mso-text-raise: -3.0pt"><?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shapetype id="_x0000_t75" stroked="f" filLED="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if linedrawn=" 0? lineDrawn? pixellinewidth="pixelLineWidth"></v:f><v:f 1? eqn="sum @0 1=" 0?></v:f><v:f eqn="sum 0=" 0? @1? 0="0"></v:f><v:f 1? eqn="prod @2 1=" 2?></v:f><v:f eqn="prod @3 21600=" pixelWidth? 21600?></v:f><v:f eqn="prod @3 21600=" 21600? pixelHeight?></v:f><v:f 1? eqn="sum @0 0=" 0?></v:f><v:f 1? eqn="prod @6 1=" 2?></v:f><v:f eqn="prod @7 21600=" pixelWidth? 21600?></v:f><v:f eqn="sum @8 21600=" 0? 21600?></v:f><v:f eqn="prod @7 21600=" 21600? pixelHeight?></v:f><v:f eqn="sum @10 21600=" 0? 21600?></v:f></v:formulas><v:path gradientshapeok="t" o:extrusi o:c></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id="_x0000_i1025" style="WIDTH: 32.25pt; HEIGHT: 14.25pt" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">机器加工,加工时间分别为每台</span><span lang="EN-US">2</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">小时和</span><span lang="EN-US">1</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">小时;生产乙机床需用</span><span lang="EN-US"><span style="POSITION: relative; TOP: 3pt; mso-text-raise: -3.0pt"><v:shape id="_x0000_i1026" style="WIDTH: 51.75pt; HEIGHT: 14.25pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz"></v:imagedata></v:shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">三种机器加工,加工时间为每台各一小时。若每天可用于加工的机器时数分别为</span><span lang="EN-US"><span style="POSITION: relative; TOP: 2pt; mso-text-raise: -2.0pt"><v:shape id="_x0000_i1027" style="WIDTH: 12pt; HEIGHT: 12.75pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz"></v:imagedata></v:shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">机器</span><span lang="EN-US">10</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">小时、</span><span lang="EN-US"><span style="POSITION: relative; TOP: 2pt; mso-text-raise: -2.0pt"><v:shape id="_x0000_i1028" style="WIDTH: 12pt; HEIGHT: 12pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz"></v:imagedata></v:shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">机器</span><span lang="EN-US">8</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">小时和</span><span lang="EN-US"><span style="POSITION: relative; TOP: 3pt; mso-text-raise: -3.0pt"><v:shape id="_x0000_i1029" style="WIDTH: 12pt; HEIGHT: 14.25pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image009.wmz"></v:imagedata></v:shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">机器</span><span lang="EN-US">7</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">小时,问该厂应生产甲、乙机床各几台,才能使总利润最大?</span></p>
<p><br/>&nbsp;</p>
<p>&nbsp; </p>
<p class="MsoNormal" style="TEXT-ALIGN: center" align="center"><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">第二章</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><span style="mso-spacerun: yes">&nbsp; </span></span></b><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">整数规划</span></b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">§1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">概论</span></p>
<p class="MsoNormal" style="MARGIN-LEFT: 24pt"><span lang="EN-US">1.1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">定义</span></p>
<p class="MsoBodyTextIndent"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">规划中的变量(部分或全部)限制为整数时,称为整数规划。若在线性规划模型中,变量限制为整数,则称为整数线性规划。目前所流行的求解整数规划的方法,往往只适用于整数线性规划。目前还没有一种方法能有效地求解一切整数规划。</span></p>
<p class="MsoBodyTextIndent" style="MARGIN-LEFT: 42pt; TEXT-INDENT: -18pt; mso-char-indent-count: 0; tab-stops: list=" l0="l0" mso-list: 42.0pt; list? lfo1? level2="level2"><span lang="EN-US" style="mso-fareast-font-family: 'Times new=" Roman?? New?><span style="mso-list: Ignore">1.2<span style="FONT: 7pt="7pt"  =" Roman?? ?Times 7pt? new="New">&nbsp;&nbsp; </span></span></span><span lang="EN-US"><span style="mso-spacerun: yes">&nbsp;&nbsp;</span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">整数规划的分类</span></p>
<p class="MsoBodyTextIndent"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">如不加特殊说明,一般指整数线性规划。对于整数线性规划模型大致可分为两类:</span></p>
<p class="MsoBodyTextIndent"><span lang="EN-US">1<sup>o </sup></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">变量全限制为整数时,称纯(完全)整数规划。</span></p>
<p class="MsoBodyTextIndent"><span lang="EN-US">2<sup>o </sup></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">变量部分限制为整数的,称混合整数规划。</span></p>
<p class="MsoBodyTextIndent"><span lang="EN-US">3<sup>o</sup> </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">变量只能取</span><span lang="EN-US">0</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">或</span><span lang="EN-US">1</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">时,称之为</span><span lang="EN-US">0-1</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">整数规划。</span></p>
<p class="MsoBodyTextIndent"><sup><span lang="EN-US"><span style="mso-spacerun: yes">&nbsp;</span></span></sup><span lang="EN-US"><span style="mso-spacerun: yes">&nbsp;</span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">整数规划特点</span></p>
<p class="MsoBodyTextIndent"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">(</span><span lang="EN-US"><span style="mso-no-proof: yes">i</span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">)</span> <span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">原线性规划有最优解,当自变量限制为整数后,其整数规划解出现下述情况:</span></p>
<p class="MsoBodyTextIndent"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? yes? mso-no-proof: new="New">①</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">原线性规划最优解全是整数,则整数规划最优解与线性规划最优解一致。</span></p>
<p class="MsoBodyTextIndent"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? yes? mso-no-proof: new="New">②</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">整数规划无可行解。</span></p>&nbsp;
<p class="MsoNormal" style="TEXT-ALIGN: center" align="center"><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">第三章</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><span style="mso-spacerun: yes">&nbsp; </span></span></b><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">非线性规划</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">§</span><span lang="EN-US">1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">非线性规划</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span lang="EN-US">1.1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">非线性规划的实例与定义</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">如果目标函数或约束条件中包含非线性函数,就称这种规划问题为非线性规划问题。一般说来,解非线性规划要比解线性规划问题困难得多。而且,也不象线性规划有单纯形法这一通用方法,非线性规划目前还没有适于各种问题的一般算法,各个方法都有自己特定的适用范围。</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">下面通过实例归纳出非线性规划数学模型的一般形式,介绍有关非线性规划的基本概念。</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times new=" Roman?? New?>例<span lang="EN-US">1<span style="mso-spacerun: yes">&nbsp; </span></span>(投资决策问题)某企业有<span lang="EN-US"><span style="POSITION: relative; TOP: 3pt; mso-text-raise: -3.0pt"><v:shapetype id="_x0000_t75" stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if linedrawn=" 0? lineDrawn? pixellinewidth="pixelLineWidth"></v:f><v:f 1? eqn="sum @0 1=" 0?></v:f><v:f eqn="sum 0=" 0? @1? 0="0"></v:f><v:f 1? eqn="prod @2 1=" 2?></v:f><v:f eqn="prod @3 21600=" pixelWidth? 21600?></v:f><v:f eqn="prod @3 21600=" 21600? pixelHeight?></v:f><v:f 1? eqn="sum @0 0=" 0?></v:f><v:f 1? eqn="prod @6 1=" 2?></v:f><v:f eqn="prod @7 21600=" pixelWidth? 21600?></v:f><v:f eqn="sum @8 21600=" 0? 21600?></v:f><v:f eqn="prod @7 21600=" 21600? pixelHeight?></v:f><v:f eqn="sum @10 21600=" 0? 21600?></v:f></v:formulas><v:path gradientshapeok="t" o:extrusi o:c></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id="_x0000_i1025" style="WIDTH: 9.75pt; HEIGHT: 11.25pt" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape></span></span>个项目可供选择投资,并且至少要对其中一个项目投资。已知该企业拥有总资金<span lang="EN-US"><span style="POSITION: relative; TOP: 2pt; mso-text-raise: -2.0pt"><v:shape id="_x0000_i1026" style="WIDTH: 12pt; HEIGHT: 12.75pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz"></v:imagedata></v:shape></span></span>元,投资于第<span lang="EN-US"><span style="POSITION: relative; TOP: 5pt; mso-text-raise: -5.0pt"><v:shape id="_x0000_i1027" style="WIDTH: 62.25pt; HEIGHT: 15.75pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz"></v:imagedata></v:shape></span></span>个项目需花资金<span lang="EN-US"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt"><v:shape id="_x0000_i1028" style="WIDTH: 12pt; HEIGHT: 18pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz"></v:imagedata></v:shape></span></span>元,并预计可收益<span lang="EN-US"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt"><v:shape id="_x0000_i1029" style="WIDTH: 11.25pt; HEIGHT: 18pt" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image009.wmz"></v:imagedata></v:shape></span></span>元。试选择最佳投资方案。&nbsp; </p>
<p class="MsoNormal" style="TEXT-ALIGN: center" align="center"><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">第四章</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><span style="mso-spacerun: yes">&nbsp; </span></span></b><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">动态规划</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">§</span><span lang="EN-US">1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">引言</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span lang="EN-US">1.1<span style="mso-spacerun: yes">&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">动态规划的发展及研究内容</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">动态规划(</span><span lang="EN-US">dynamic programming</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">)是运筹学的一个分支,是求解多阶段决策问题的最优化方法。</span><span lang="EN-US">20</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">世纪</span><span lang="EN-US">50</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年代初</span><span lang="EN-US">R. E. Bellman</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">等人在研究多阶段决策过程</span><span lang="EN-US">(multistep decision process)</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">的优化问题时,提出了著名的最优性原理(</span><span lang="EN-US">principle of optimality</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">),把多阶段过程转化为一系列单阶段问题,逐个求解,创立了解决这类过程优化问题的新方法—动态规划。</span><span lang="EN-US">1957</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年出版了他的名著《</span><span lang="EN-US">Dynamic Programming</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">》,这是该领域的第一本著作。</span></p>
<p class="MsoBodyTextIndent2" style="TEXT-INDENT: 21pt"><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">动态规划问世以来,在经济管理、生产调度、工程技术和最优控制等方面得到了广泛的应用。例如最短路线、库存管理、资源分配、设备更新、排序、装载等问题,用动态规划方法比用其它方法求解更为方便。</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; mso-bidi-font-size: 12.0pt"><o:p></o:p></span></p>
<p class="MsoBodyTextIndent2" style="TEXT-INDENT: 21pt"><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">虽然动态规划主要用于求解以时间划分阶段的动态过程的优化问题,但是一些与时间无关的静态规划(如线性规划、非线性规划),只要人为地引进时间因素,把它视为多阶段决策过程,也可以用动态规划方法方便地求解。</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; mso-bidi-font-size: 12.0pt"><o:p></o:p></span></p>
<p class="MsoNormal" style="TEXT-INDENT: 24pt"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">应指出,动态规划是求解某类问题的一种方法,是考察问题的一种途径,而不是一种特殊算法(如线性规划是一种算法)。因而,它不象线性规划那样有一个标准的数学表达式和明确定义的一组规则,而必须对具体问题进行具体分析处理。因此,在学习时,除了要对基本概念和方法正确理解外,应以丰富的想象力去建立模型,用创造性的技巧去求解。</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0">&nbsp; </p>
<p class="MsoNormal" style="TEXT-ALIGN: center" align="center"><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">第五章</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><span style="mso-spacerun: yes">&nbsp; </span></span></b><b><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 12.0pt? new="New">图与网络模型及方法</span></b><b><span lang="EN-US" style="FONT-SIZE: 14pt; mso-bidi-font-size: 12.0pt"><o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">§</span><span lang="EN-US">1 </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">概论</span></p>
<p class="MsoNormal"><span lang="EN-US"><span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">图论起源于</span><span lang="EN-US">18</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">世纪。第一篇图论论文是瑞士数学家欧拉于</span><span lang="EN-US">1736 </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年发表的“哥尼斯堡的七座桥”。</span><span lang="EN-US">1847</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年,克希霍夫为了给出电网络方程而引进了“树”的概念。</span><span lang="EN-US">1857</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年,凯莱在计数烷</span><span lang="EN-US"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt"><v:shapetype id="_x0000_t75" stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if linedrawn=" 0? lineDrawn? pixellinewidth="pixelLineWidth"></v:f><v:f 1? eqn="sum @0 1=" 0?></v:f><v:f eqn="sum 0=" 0? @1? 0="0"></v:f><v:f 1? eqn="prod @2 1=" 2?></v:f><v:f eqn="prod @3 21600=" pixelWidth? 21600?></v:f><v:f eqn="prod @3 21600=" 21600? pixelHeight?></v:f><v:f 1? eqn="sum @0 0=" 0?></v:f><v:f 1? eqn="prod @6 1=" 2?></v:f><v:f eqn="prod @7 21600=" pixelWidth? 21600?></v:f><v:f eqn="sum @8 21600=" 0? 21600?></v:f><v:f eqn="prod @7 21600=" 21600? pixelHeight?></v:f><v:f eqn="sum @10 21600=" 0? 21600?></v:f></v:formulas><v:path gradientshapeok="t" o:extrusi o:c></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id="_x0000_i1025" style="WIDTH: 42.75pt; HEIGHT: 18pt" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">的同分异构物时,也发现了“树”。哈密尔顿于</span><span lang="EN-US">1859</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">年提出“周游世界”游戏,用图论的术语,就是如何找出一个连通图中的生成圈,近几十年来,由于计算机技术和科学的飞速发展,大大地促进了图论研究和应用,图论的理论和方法已经渗透到物理、化学、通讯科学、建筑学、生物遗传学、心理学、经济学、社会学等学科中。</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 21pt; mso-char-indent-count: 2.0"><span lang="EN-US"><o:p>&nbsp; </p>
<p class="MsoNormal" style="TEXT-ALIGN: center" align="center"><b><span style="FONT-SIZE: 24pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" ?Times mso-hansi-font-family: Roman?; New? mso-bidi-font-size: 10.0pt? new="New">初等数学方法建模</span></b><b><span lang="EN-US" style="FONT-SIZE: 24pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><span style="mso-spacerun: yes">&nbsp; </span></span></p>
<p class="MsoNormal" style="TEXT-INDENT: 10.5pt; mso-char-indent-count: 1.0"><span lang="EN-US"><span style="mso-spacerun: yes">&nbsp;</span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">现实世界中有很多问题,它的机理较简单,用静态</span><span lang="EN-US">,</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">线性或逻辑的方法即可建立模型,使用初等的数学方法,即可求解,我们称之为初等数学模型。本章主要介绍有关自然数,比例关系,状态转移,及量刚分析等建模例子,这些问题的巧妙的分析处理方法,可使读者达到举一反三,开拓思路,提高分析</span><span lang="EN-US">, </span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times new=" Roman?? ?Times mso-hansi-font-family: Roman?; New? new="New">解决实际问题的能力。</span></p></o:p></span></span>
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[此贴子已经被作者于2008-6-18 14:02:11编辑过]
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最近下载过的用户(2)
· 2008-10-3 22:44:30
thanks
· 2009-3-25 11:28:52
<p>谢谢,正好要用呢~~~</p>
· 2009-4-21 23:37:03
<p>谢谢楼主了</p>
· 2009-5-27 08:23:13
怎么老下不下来啊
· 2009-6-4 19:18:23
多谢了
· 2009-6-12 10:50:38
[BR]这东西对我有用
· 2009-6-12 10:51:24
好像下不了啊怎么回事啊
· 2011-12-18 22:22:33
???在哪下?
· 2012-5-20 18:39:00
很厉害,哈哈,也很哟御用的东西
· 2020-4-28 16:55:43
谢谢楼主分享资料

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